# Project Euler 195
# Count 60-degree integer triangles with inradius r <= 1053779.
import euler.nt { isqrt, gcd }
function T(N: i64) -> i64 {
let N2: i64 = N * N
let p1_max: i64 = isqrt((4 * N2) / 3)
let p2_max: i64 = isqrt(12 * N2)
let num1: i64 = 4 * N2
let num2: i64 = 12 * N2
let mut total: i64 = 0
let mut m: i64 = 2
while m <= p1_max {
let mut n_lim: i64 = p1_max / m
if n_lim >= m { n_lim = m - 1 }
let mut n: i64 = 1
while n <= n_lim {
if (m - n) % 3 != 0 && gcd(m, n) == 1 {
let p: i64 = m * n
total = total + isqrt(num1 / (3 * p * p))
}
n = n + 1
}
m = m + 1
}
let m_max2: i64 = (p2_max + 2) / 3
m = 2
while m <= m_max2 {
let D: i64 = 9 * m * m - 8 * p2_max
let mut lo1: i64 = 1
let mut hi1: i64 = m - 1
let mut lo2: i64 = 0
let mut hi2: i64 = -1
if D > 0 {
let s: i64 = isqrt(D)
let r1: i64 = (3 * m - s) / 4
let r2: i64 = (3 * m + s + 3) / 4
if r2 > r1 + 1 {
hi1 = r1
if hi1 > m - 1 { hi1 = m - 1 }
if r1 < 1 { hi1 = 0; lo1 = 1 }
lo2 = r2
hi2 = m - 1
if lo2 > hi2 { lo2 = 0; hi2 = -1 }
}
}
# range 1
if lo1 <= hi1 {
let mut d: i64 = lo1
while d <= hi1 {
if d % 3 != 0 && gcd(m, d) == 1 {
let p: i64 = d * (3 * m - 2 * d)
if p > 0 {
total = total + isqrt(num2 / (p * p))
}
}
d = d + 1
}
}
if lo2 <= hi2 {
let mut d: i64 = lo2
while d <= hi2 {
if d % 3 != 0 && gcd(m, d) == 1 {
let p: i64 = d * (3 * m - 2 * d)
if p > 0 {
total = total + isqrt(num2 / (p * p))
}
}
d = d + 1
}
}
m = m + 1
}
return total
}
function main() -> i32 {
printf("%lld\n", T(1053779))
return 0
}
Generated C
#include <stdint.h>
#include <stdbool.h>
#include <stdio.h>
#include <stdlib.h>
#include <string.h>
/* Flow runtime helpers */
typedef struct flow_temp_node { struct flow_temp_node* next; } flow_temp_node;
static flow_temp_node* flow_temp_head = NULL;
static int flow_temp_atexit_set = 0;
__attribute__((unused)) static void flow_temp_free_all(void) {
while (flow_temp_head) {
flow_temp_node* n = flow_temp_head;
flow_temp_head = n->next;
free(n);
}
}
__attribute__((unused)) static void* flow_temp_alloc(size_t nbytes) {
flow_temp_node* node = (flow_temp_node*)malloc(sizeof(flow_temp_node) + nbytes);
if (!node) return NULL;
node->next = flow_temp_head;
flow_temp_head = node;
if (!flow_temp_atexit_set) {
flow_temp_atexit_set = 1;
atexit(flow_temp_free_all);
}
return (void*)(node + 1);
}
#ifndef FLOW_DIAG
#define FLOW_DIAG(msg) fprintf(stderr, "%s", (msg))
#endif
#ifndef FLOW_LOG
#define FLOW_LOG(fmt, ...) printf(fmt, __VA_ARGS__)
#endif
#ifndef FLOW_LOG_EMPTY
#define FLOW_LOG_EMPTY(fmt) printf(fmt)
#endif
static char* flow_strcat(const char* a, const char* b) {
size_t la = strlen(a ? a : ""), lb = strlen(b ? b : "");
char* r = (char*)flow_temp_alloc(la + lb + 1);
if (!r) return NULL;
if (la) memcpy(r, a, la);
if (lb) memcpy(r + la, b, lb);
r[la + lb] = '\0';
return r;
}
#define __flow_in_arr(arr, val) __extension__ ({ \
int _found = 0; \
size_t _n = sizeof(arr)/sizeof((arr)[0]); \
for (size_t _i = 0; _i < _n; _i++) { \
if ((arr)[_i] == (val)) { _found = 1; break; } \
} _found; })
/* Unified fault handler (MISRA #279) — override with -DFLOW_FAULT_HANDLER=fn */
#ifndef FLOW_FAULT_HANDLER
__attribute__((unused)) static inline void flow_fault_handler(const char* msg) {
fprintf(stderr, "flow: %s\n", msg ? msg : "fault");
abort();
#if defined(__GNUC__) || defined(__clang__)
__builtin_unreachable();
#endif
}
#else
#define flow_fault_handler FLOW_FAULT_HANDLER
#endif
#define flow_div_by_zero_handler() flow_fault_handler("division by zero")
#define flow_shift_ub_handler() flow_fault_handler("invalid shift (amount out of range or left-shift of negative)")
#ifndef FLOW_CHECKED_DIV
#define FLOW_CHECKED_DIV(L, R) (((R) != 0) ? ((L) / (R)) : (flow_div_by_zero_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_MOD
#define FLOW_CHECKED_MOD(L, R) (((R) != 0) ? ((L) % (R)) : (flow_div_by_zero_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_SHL
#define FLOW_CHECKED_SHL(L, R) ((((R) >= 0) && ((unsigned long long)(R) < (sizeof(L) * 8ull)) && ((L) >= 0)) ? ((L) << (R)) : (flow_shift_ub_handler(), (L) * 0))
#endif
#ifndef FLOW_CHECKED_SHR
#define FLOW_CHECKED_SHR(L, R) ((((R) >= 0) && ((unsigned long long)(R) < (sizeof(L) * 8ull))) ? ((L) >> (R)) : (flow_shift_ub_handler(), (L) * 0))
#endif
#include <math.h>
void* _ui_state = NULL;
static inline float i32_to_f32(int32_t v) { return (float)v; }
/* Host stub for @gpu kernels (device codegen replaces this). */
static inline int32_t gpu_thread_id(void) { return 0; }
int64_t gcd_i64_i64(int64_t a0, int64_t b0);
int64_t lcm_i64_i64(int64_t a, int64_t b);
int64_t isqrt_i64(int64_t n);
int64_t mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod);
int64_t mod_pow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod);
bool is_prime_i64(int64_t n);
int64_t T_i64(int64_t N);
int32_t main(void);
int64_t gcd_i64_i64(int64_t a0, int64_t b0) {
int64_t a = a0;
int64_t b = b0;
while (b != 0) {
int64_t t = FLOW_CHECKED_MOD((a), (b));
a = b;
b = t;
}
return a;
}
int64_t lcm_i64_i64(int64_t a, int64_t b) {
if ((a == 0 || b == 0)) {
return 0;
}
return (FLOW_CHECKED_DIV((a), (gcd_i64_i64(a, b))) * b);
}
int64_t isqrt_i64(int64_t n) {
if (n < 2) {
return n;
}
int64_t x = n;
int64_t y = FLOW_CHECKED_DIV(((x + 1)), (2));
while (y < x) {
x = y;
y = FLOW_CHECKED_DIV(((x + FLOW_CHECKED_DIV((n), (x)))), (2));
}
return x;
}
int64_t mulmod_i64_i64_i64(int64_t a0, int64_t b0, int64_t mod) {
int64_t a = FLOW_CHECKED_MOD((a0), (mod));
int64_t b = FLOW_CHECKED_MOD((b0), (mod));
int64_t result = 0;
while (b > 0) {
if (FLOW_CHECKED_MOD((b), (2)) == 1) {
result = FLOW_CHECKED_MOD(((result + a)), (mod));
}
a = FLOW_CHECKED_MOD(((a * 2)), (mod));
b = FLOW_CHECKED_DIV((b), (2));
}
return result;
}
int64_t mod_pow_i64_i64_i64(int64_t base, int64_t exp, int64_t mod) {
if (mod == 1) {
return 0;
}
int64_t result = 1;
int64_t b = FLOW_CHECKED_MOD((base), (mod));
int64_t e = exp;
while (e > 0) {
if (FLOW_CHECKED_MOD((e), (2)) == 1) {
result = mulmod_i64_i64_i64(result, b, mod);
}
b = mulmod_i64_i64_i64(b, b, mod);
e = FLOW_CHECKED_DIV((e), (2));
}
return result;
}
bool is_prime_i64(int64_t n) {
if (n < 2) {
return 0;
}
if (n < 4) {
return 1;
}
if ((FLOW_CHECKED_MOD((n), (2)) == 0 || FLOW_CHECKED_MOD((n), (3)) == 0)) {
return 0;
}
int64_t i = 5;
while ((i * i) <= n) {
if ((FLOW_CHECKED_MOD((n), (i)) == 0 || FLOW_CHECKED_MOD((n), ((i + 2))) == 0)) {
return 0;
}
i = (i + 6);
}
return 1;
}
int64_t T_i64(int64_t N) {
int64_t N2 = (N * N);
int64_t p1_max = isqrt_i64(FLOW_CHECKED_DIV(((4 * N2)), (3)));
int64_t p2_max = isqrt_i64((12 * N2));
int64_t num1 = (4 * N2);
int64_t num2 = (12 * N2);
int64_t total = 0;
int64_t m = 2;
while (m <= p1_max) {
int64_t n_lim = FLOW_CHECKED_DIV((p1_max), (m));
if (n_lim >= m) {
n_lim = (m - 1);
}
int64_t n = 1;
while (n <= n_lim) {
if ((FLOW_CHECKED_MOD(((m - n)), (3)) != 0 && gcd_i64_i64(m, n) == 1)) {
int64_t p = (m * n);
total = (total + isqrt_i64(FLOW_CHECKED_DIV((num1), (((3 * p) * p)))));
}
n = (n + 1);
}
m = (m + 1);
}
int64_t m_max2 = FLOW_CHECKED_DIV(((p2_max + 2)), (3));
m = 2;
while (m <= m_max2) {
int64_t D = (((9 * m) * m) - (8 * p2_max));
int64_t lo1 = 1;
int64_t hi1 = (m - 1);
int64_t lo2 = 0;
int64_t hi2 = (-1);
if (D > 0) {
int64_t s = isqrt_i64(D);
int64_t r1 = FLOW_CHECKED_DIV((((3 * m) - s)), (4));
int64_t r2 = FLOW_CHECKED_DIV(((((3 * m) + s) + 3)), (4));
if (r2 > (r1 + 1)) {
hi1 = r1;
if (hi1 > (m - 1)) {
hi1 = (m - 1);
}
if (r1 < 1) {
hi1 = 0;
lo1 = 1;
}
lo2 = r2;
hi2 = (m - 1);
if (lo2 > hi2) {
lo2 = 0;
hi2 = (-1);
}
}
}
if (lo1 <= hi1) {
int64_t d = lo1;
while (d <= hi1) {
if ((FLOW_CHECKED_MOD((d), (3)) != 0 && gcd_i64_i64(m, d) == 1)) {
int64_t p = (d * ((3 * m) - (2 * d)));
if (p > 0) {
total = (total + isqrt_i64(FLOW_CHECKED_DIV((num2), ((p * p)))));
}
}
d = (d + 1);
}
}
if (lo2 <= hi2) {
int64_t d = lo2;
while (d <= hi2) {
if ((FLOW_CHECKED_MOD((d), (3)) != 0 && gcd_i64_i64(m, d) == 1)) {
int64_t p = (d * ((3 * m) - (2 * d)));
if (p > 0) {
total = (total + isqrt_i64(FLOW_CHECKED_DIV((num2), ((p * p)))));
}
}
d = (d + 1);
}
}
m = (m + 1);
}
return total;
}
int32_t main(void) {
printf("%lld\n", T_i64(1053779));
return 0;
}